Many, many sources provide access to different types of qualitative data. A few are listed below, but be aware that the diversity of potential types of source records produces data that are difficult to compile in a single list.
National and Official Archives
US National Archives and Records Administration (NARA): https://www.archives.gov/research
UK National Archives: https://www.nationalarchives.gov.uk/help-with-your-research/start-here/
Library and Archives Canada (LAC): https://www.canada.ca/en/library-archives/collection/research-help.html
National Archives of Australia (NAA): https://www.naa.gov.au/help-your-research/getting-started
In the US, state and local governments also hold their own archives, which may be more accessible to you than federal deposits. NARA provides a consolidated collection at https://www.archives.gov/research/alic/reference/state-archives.html . The Presidential Libraries hold collections from their named presidents and also from other actors or organizations that were involved in the administration (so, the personal papers of, say, the Secretary of State, as opposed to the official papers of the same individual). Agan, NARA has a consolidated set of links at https://www.archives.gov/findingaid/presidential-library-explorer/list?_ga=2.8022450.1421537562.1755016459-1037409017.1755016459 .
Other sources of access
In the US, the National Security Archive is a nonprofit that files Freedom of Information Act (FOIA) requests with federal agencies and then curates and publishes the resultant documents. Most of its documents are in collections published as microfiche, which must be viewed on a special machine in the library, but some selected items are made freely available as electronic briefing books at their site, https://nsarchive.gwu.edu/ .
In the UK, Westminster Foundation for Democracy files and collects FOIA requests on a broader collection of topics. You can browse their work at https://www.wfd.org/governance/freedom-information.
For historical documentation of foreign policy, most larger developed countries produce declassified document collections that are curated by year and often by theme. These series include the Foreign Relations of the United States (https://history.state.gov/historicaldocuments). The UK’s documentary history is more complex; see https://guides.library.upenn.edu/c.php?g=475913 for guidance on how to locate specific elements. Those with reading familiarity in other languages can exploit that; France’s Ministry of Foreign Affairs has an excellent collection online at https://www.diplomatie.gouv.fr/fr/archives-diplomatiques/ . Readers of German will find many useful resources at https://archiv.diplo.de/arc-de/das-politische-archiv. You can find a mostly-comprehensive list of countries that publish declassified diplomatic documents at https://diplomatic-documents.org/editions/ .
Oral History
The US Library of Congress has an extensive collection of oral histories, including on civil rights and veterans. See https://libguides.rutgers.edu/c.php?g=933713&p=6731986 for a guide to accessing and using LOC and other collections.
Subscription Services
OCLC ArchivesGrid is a subscription service that your university library may subscribe to. It collects information on what kinds of special holdings libraries and other archives have. Some of these have electronic resources available. It is more useful, however, for advanced researchers who can travel for research and are looking to find specific holdings.
ProQuest’s Historical Newspapers collection is another subscription database. It contains full text of a very diverse range of historical newspapers, both American and international, reproduced in their original language. Subscription is fairly widespread, at least to the lower tiers of service, and it’s very useful for understanding what people actually knew at any point in time and how they were talking or thinking about it.